Android 14 prepares to let you save an 'app pair' that launches side-by-side in split-screen mode!
In Beta 2, a new launcher flag has been added that, when enabled, surfaces a "save app pair" menu item in the context menu of split-screened apps in the recents overview.
Currently, tapping "save app pair" doesn't work, but when the feature is ready, I'm guessing this will let you add a shortcut to the home screen to launch two apps in split-screen mode.